A rectangular coil has a long straight wire passing through its centroid perpendicular to its plane as shown. If current through the wire varies as \[i={{i}_{0}}\sin \omega t\], induced current in the coil will be (Given R = Resistance of the coil)

• A. \[\frac{{{i}_{0}}\sin \omega t}{R}\]       
• B. \[\frac{\pi a\sin \omega t}{bR}\]
• C. zero
• D. \[\frac{\pi a\cos \omega t}{bR}\]